We prove a boundary Harnack type inequality for non-negative solutions to singular equations of $p$-parabolic type, $2n/(n + 1) < p < 2$, in time-independent cylinder whose base is $C^{1,1}$-regular. Simple examples show, using the corresponding estimates valid for the heat equation as a point of reference, that this type of inequalities can not, in general, be expected to hold in the degenerate case ($2 < p < ∞$)